Egg Group

Egg Group is a classification used in the Pokémon games that defines how Pokémon can breed. Depending on the Pokémon that bred the offspring (who will be born in an egg) can acquire new skills that they normally wouldn't be able to learn. If two Pokémon are not in an identical Egg Group, they cannot breed at all. This is the list of all egg groups:

Undiscovered: The Pokémon in this group simply cannot breed whatsoever, not even with Ditto.

Ditto: Ditto, thanks to its transformation abilities, is able to breed with almost any Pokémon (regardless of gender), excluding the Pokémon in the Undiscovered group or another Ditto.

Grass: Egg group 1. All the Pokémon in this egg group are Grass types.

Mineral: Egg group 5. The Pokémon in this group are unorganic in nature. Most of this group's Pokémon are Ice, Rock, Steel or Ground types.

Amorphous: Egg group 6. The Pokémon in this group are amorphous, having no defined form. Most of this group's Pokémon are Psychic, Poison and Ghost types.

Field: Egg group 7. The Pokémon in this group are terrestrial in nature. It has a large variety of Pokémon.

Water 1: Egg group 8. One of three Water egg groups. Many of these Pokémon have extremities that allow them to live on land.

Water 2: Egg group 9. Most of the Pokémon in this group don't have extremities but instead, they have fins.

Water 3: Egg group 10. The Pokémon in this group are mainly arthropods and fossils. The arthropodos are a group of invertebrates where we can find crustaceans and arachnids.

Monster: Egg group 11. The appearance of Pokémon in this group is beast-, dinosaur- or reptile-like.

Fairy: Egg group 12. The Pokémon in this group are mainly considered petite and very cute. After Generation VI onwards, many of these Pokémon are precisely Fairy types.

Dragon: Egg group 13. The Pokémon is this group are mainly Dragon types. There are Pokémon that have appearence of dragons, serpents, lizards, or similar reptiles, without necessarily being Dragon-type Pokémon.

Breeding

During the breeding, the father must have the moves to pass on to the baby, and the mother must be the species of Pokémon desired. The only exception to this rule is between Nidoran♀ and Nidoran♂, where the baby can be 50/50 male or female. In some instances, chain breeding is needed to pass down moves from generation to generation. If the two Pokémon who have the baby are the same speicies, the egg will come quicker.

Any move that can be learned as an egg move, be it TM, HM, or other, it will be passed on to the offspring.